Martin Flashman's Courses
Math 109 Calculus I Spring, '03
MTRF  11:00-11:50 SH 115
Check Blackboard for Reality Quizzes 23, 24 and 25!

Final examination will be allowed 2 hours.
CHECKLIST FOR REVIEW + Bonus Problem
Review session in LIB 56: Sunday 3-5
 
 
Final Examination Self-Schedule Spring, 2003
Time
Monday
Tuesday
Wednesday
Thursday 
Friday
1020-1220
Room: SH 116 
Room: SH 116 
Math 109 Scheduled
Room: SH 116
Room: SH116 
Math 210 Scheduled
No Exams
1300-1500
Room: TBA
Room:TBA
Room: TBA
No Exams
Office Hours 
[1400-1600]
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1500-1700
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Room: TBA
 




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Last updated: 1/27/03
Spring, 2003               MATH 109 : CALCULUS I         M.FLASHMAN 
Stewart's Calculus 4th ed'n. 
Assignments and recommended problems (tentative- subject to change!) 
Date Due Reading Problems ( *= interesting but optional) Optional Viewing: Ed Berger CD Tutorial 
[# of minutes] 
* means optional
1-24 1.1 1,2,10,13,15,17,21,22,45, 47, 48, 51, 53 Introduction;  
How to Do Math
1-27 0.B2 [on-line] 

Appendix B
rev. sheet (on-line): 1-3,6,13,15,16,18,19 

pg. A-15: 7-10; 17-20; 21-35 odd; 62
On-line Mapping Figure Activities Functions [19]
1-28 1.2 1-5;8,10,11   Average Rates of Change [11]
1-30 1.3   3;5; 54, 55 *65 The Two Questions of Calculus [10] 
1-28 0.B2 [on-line] # 19, 20, 21
1-30 1.4 1,3,37   Parabolas [22]
1-31 0.C [on-line] [Models and Mathematics- Probability ]  
1-31 2.1 Geom (i)1,2,4   Slope of a Tangent Line [12] 
2-3 2.1 Motion  (ii) 5,8  Rates of Change, Secants and Tangents [19] 
2-3 DO NOT Read 2.6 p121,122: 1(a),2(a),3,5(a[ignore i and ii.Use 4steps as in class],b),6(a[ignore i and ii.Use 4steps as in class],b),9   
2-10 Summary of weeks 1-3 due by 5 pm
2-4 2.6 Use the 4 steps method with x or t = a when appropriate in 11,13,17-19; 15 Finding Instantaneous Velocity [20]
2-6(i) 
2-7(ii)&(iii)
3.1 (i)1,7, 13-16 Use the 4 steps method to find f '(a)  
(ii) 2,3, 8,26,29  
(iii)11,19-21,23
  Equation of a Tangent Line [18]
2-10 (i) 3.2 (i)1,3-7; 17-23 odd 
(ii) 31,32,37,42
 (ii) 41 (i)The Derivative [12] 
The Derivative of the Reciprocal Function [18] 
(ii)Differentiability [3]
2-10 
2-14 and 17(Review again!)
Appendix D 
Especially formulae 6-8,10,12,13
 
Optional CH. 5.1-5.3 - TRIGONOMETRIC       FUNCTIONS (VIDEO)PRECALCULUS #8 
CH. 5.4-5.6 - TRIGONOMETRIC      FUNCTIONS (VIDEO) PRECALCULUS #9
Review of trigonometry on reserve in the library for Math 115.
2-11 (i) 
2-17(ii) 
2-18(iii)
3.4 (i) p 158-160 
(ii)161-162, 165-166
(i) 1-3;11 
(ii) 23,27,28 
(iii) 12, 16, 20, 31 
 (ii)*33 (i) Instantaneous Rate [15] 
(ii)More on Instantaneous Rate [19] 
2-11(i) 
2-13(ii) 
2-14 (iii) 
2-17 (iv)
3.3(i) p 147-150 
(ii)p 151-152 
(iii) p 152-155
(i)1-5, 7-15 odd, 28-30,43 
(ii) 8-16 even, 19-22; 55a, 56(a,b), 59a, 61-63, 66-68 
(iii) 83, 18, 23-25, 31 
(iv)49, 53, 54, 55 (b,c), 58, 65, 73
*74 
*The Derivative of  the Square Root [16] 
(i) Uses of The Power Rule [20] 
(ii) Short Cut for Finding Derivatives [14] (iii)The Product Rule [21] 
(iv)The Quotient Rule [13] 
2-18(i) 
2-20(ii) 
2-21(iii)
3.5 (i) pp170-173 
(ii)pp 173-174 
(iii)p175. 

Read web materials on trigonometric derivatives.

(i) 1-3,5,10,11,13,22,23,28,31 
(ii) 4,6,9,21,26,33,45a 
(iii)READ Examples 4 and 5 first! 35,36,38,39,43 
(ii) *34 *Review of Trig[12] 
*Graphing Trig Functions[17] 
(i)The derivatives of trig functions [14]
2-21 Read on-line  
Sens. Calc. 0.C on Probability Models
2-24 (i) 
2-25(ii)
3.6 The Chain Rule 
(i) pp177-179 only! 
(ii) pp181,182
(i) 7-14 use Leibniz notation. 
(ii) 16, 17,21,27,31,37 
(iii) 45,51,53,55, 59, 63
(iii)*57,*70 (i) Introduction to The Chain Rule [18] 
(ii)Using the Chain Rule [13]
2-25 (ii) 
2-27 (iii)
3.2(ii)p 142Example 6 
(iii)p142-3. Differentiability and continuity 
(ii)33 
(iii) 31,32,37
(ii) 41 (ii)Differentiability [3]
3-3 Read on-line  
Sens. Calc. I.C.1 on Probability Models
2-28(i)READ(&View) ONLY 
3-3 (i) and view (ii) 
3-4 (ii)
3.7(i) pp 185-188 
(i)Read web materials on implicit differentiation.
(i) 5-10, 15, 25, 26 
(ii) 29, 36, 37, 41, 42, 51
*38, *53 (i)Intro to Implicit Differentiation [15]  
(ii) Finding the derivative implicitly [12] 
3-3(i) Read (&view) ONLY 
3-4 (i) 
3-10(ii) 
3-10(iii)
3.9 Related rates (i) pp199-201 
(ii) pp201-203
(i)3,5,11  
(ii) 7,10,12 
(iii)16,19,31,32
(i)The Ladder Problem [14] 
(ii) The Baseball Problem[19]or The Blimp Problem [12]
2-27(i) 
3-6 (ii) 
3-7 (iii)
3.8 Higher Order Derivatives 
(i) pp192-194 
(iii)pp 195-196
(i) 1-15 odd, 21 
(ii) 43,44,47,51 
(iii)35,36, 53
(iii) *(57,62) (ii)Acceleration and the derivative.[5]
2-25 and 2-27 Read only (i) 
2-28 Do problems(i) and (ii) 
3-4 (iii) Intermediate Values
2.5 (i) pp 104-106 
(iii) pp 111-2
(i) 3,4,7,17-20 
(ii) 34,37, 38 
(iii) 41,43,45,48, 59
(iii)55, 56 (i)One Sided Limits [6] Continuity and  discontinuity [4]
3-6(i) 
3-7(ii)
4.9 
Read web materials on Newton's Method.
(i) 1,3,5-7 
(ii)11,15,16,25
(ii)*26,*27
3-11(i) 
3-13&14(ii)READ ONLY 
3-25(ii) 
4-1(iii)
3.10 (i)  205-207 
(ii) 209-210 
Read web materials on differentials 
(i) 5,7,9 
(ii) 15-17, 21-25 odd, 31,33 
(iii) 42-45
(ii)Using tangent line approximations [25] 
3-12 Examination #1  Covers all assignments through 3-10. 
Sections covered: 1.1-1.4, 2.1,2.5,2.6, 3.1-3.9,4.9 
0.B2 , 0.C
3-11(i) 
3-13 or 14(ii) 
3-14(iii)
4.1(i)pp223-227 
(ii) pp228-229 plus 
On-Line tutorial on Max/mins 
(iii) reread ... all
(i) 3-6;31-41 odd 
(ii)47,49,11,34,48 
(iii) 13, 51, 53, 57, *65
3-14(i) 
3-24(ii) 
3-25(iii) 
4-1(iv)
4.7 (i) 1,2,7 
(ii) 9, 15, 17, 29 
(iii) 24, 34, 49, 53 
(iv) 48,50
(iii)The connection between Slope and Optimization [28] 
[optional] The Box Problem [20]
3-24(i) 

3-27(ii)
4.3(i) 240-242  

(ii) 243-246
(i)5,6, 8(a,b), 11(a,b), 25(a,b), 27 (a,b) 

(ii)7,8, 11c, 17, 21-23, 25(c-d), 27(c,d), 47
(i)[Optional]{Intro to Curve Sketching [9]  
Critical Points [18] The First Derivative Test [3] 
Regions where a function is increasing...[20] } 

(ii)Using the second derivative [17] Concavity and Inflection Points[13] 
The 2nd Deriv. test [4] 
Acceleration & the Derivative [6] 
3-28 2.2 pp78-81 Vertical Asymptotes 8,9, 21-24 Domain restricted functions ...[11] Vertical asymptotes [9] 
4-1(i) 
4-1(ii)
4.4 (i) 249-255  
Horiz. Asymptotes 
(ii)
(i) 3,4, 11-15, 31-34 
(ii) 39-41, 47-49, 55, 56
(i)Horizontal asymptotes  [18] 
(ii)Graphing ...asymptotes [10]  
Functions with Asy.. and holes[ 4]  
Functions with Asy..and criti' pts [17]
4-3(i) 
4-4(ii)
4.5 Read Examples 1-3! (i) 1-11 odd, 31, 36 
(ii) 27, 32, 35, 38
(i)Graphs of Poly's [10]
4-8 (i) 
4-11(ii)
4.6 (i) Read Examples 1-3! 
(ii) Read Example 4
(i)1,7 
(ii) 10, 21
 
4-3(i) 
4-4 (ii)
4.2 (i)7,8,11,23, 25  
(ii) 15, 19, 33
(i)Three  Big Theorems [11]
4-4(i) 
4-7(ii)
IVA(On-line) 
A java graph showing 
f (x)=P'(x) related for f a cubic polynomial
(i)On line IVA:1(a,d,e,f),10 
(ii) 4, 5(a,b),8,11
(ii) 6 Antidifferentiation[14]
4-7(i) 
4-8(ii) 
4-10(iii)
4.10  (i) 1-3, 5-11 odd,15-17, 25-28 
(ii)31-37 odd,41, 53, 55, 57 [revised 4-7] 
(iii)47,51,52
(iii)Antiderivatives and Motion [20]  
Antiderivatives of powers of x [18]
4-7 IVB (On-line) Read
4-10(i) 
4-18?(ii)
10.2 (i) 620-623  
     (ii) 624-626
(i)3-6,7,9 
(ii) 19a, 21, 24
(i)*15, *17
4-8 Read only 
4-10
IVD (on-line) 1-11 odd (online)
4-11(i) 
4-14(ii)
IVE (on-line) (i)1,2 
(ii) 5 (a,b), 7(a,b), 11(a,b)
4-11 Lab assignment from 4-7 Lab assignment 4-7
4-11 IVF READ  
4-14(i) 
4-15 (ii) 
4-17(iii)
IVF(On line) (i)1,3,5,13,15,17(on-line) 
(ii) 19,21,23 (on-line) 
(iii) 33,34
4-15(i)  
4-17(ii)
VA ( On Line) NEW! (i)1,2 a (on line) 
(ii) 5(a,b)
2c
4-15(i) 
4-17(ii) 
4-18(iii) 
4-21(iv) 
4-22(v)
5.3 (i) and (ii) p342-343 
(iii) p338,340,341
(i) 17-23 odd (Use F T of Calc) 
(ii) 18,20,22,29,31,35,37 
(iii)  39 
(iv) 5,7,12, 13 49 
(v)51
(iv)56 (iv)The Fundamental theorem[17]  
Illustrating the FT[14]  
Evaluating Definite Integrals [13]
4-18 Appendix E p.A34 
Sum Notation
pA38:1-4,11-13,17,18
4-18(i) 
4-21(ii)&(iii)
5.4 (i)and (ii)p347-350 
(iii)351-352
(i) 1-9 odd,10 
(ii)17-27 odd, 45 
(iii) 47-51 odd,53,55
4-21 Summary due.
4-23 
Self Scheduled
Examination #2 Covers all assignments though 4-18 (Mainly material not covered in Examination #1)Tentative sections covered: 3.10, 4.1-4.7, 4.10, 10.2, IVA, IVB, IVD, IVE, VA, 5.3, 5.4, and Appendix E.
4-22(i) 
4-29(ii)
5.5 (i) 356-358 
(ii) 359-361
(i) 1-4; 7-13 odd; 
(ii)17-23; 37-41
(i)Undoing the chain rule.[9]  
(i)Integrating polynomials by Substitution [15] 
4-24(i) 
5-1(ii)
5.2 (i) p324-326; Example 2a; 330-331. 
(ii)331-334
(i)2,5,6,7,8,15-18,29 
(ii)31-35(odd);39,43-46,47-57(odd),63
*30 
4-24 6.5 1,3,5,13-15 Finding the Average Value of a Function [8]
4-28(i) 
4-29(ii) 
5-1(iii)
6.1 (i) pages 371-374  
(ii) pages 374-376
(i) 1,2,7,11,15,16  
(ii)3,4,17, 19, 45 
(iii) 29,33,39,41
*47 (i)Area between two curves [9] 
Limits of integration-Area [15]
5-1(i)Read only! 
5-2(i) 
5-5(ii) 
5-8(iii)
6.2 (i) pp 378-381  
(ii) pp 381-384 
(iii)p 385-386
(i)1,3,4,7 
(ii) 5,10,19,23, 31, 32 
(iii)  39, 40,51,52
*61,*59 (i)Finding volumes using cross sectional slices. 
Solids of revolution 
(ii)The disc method along the y-axis. 
The washer methods...
6.3 (i)1, 3, 7, 8, 28 
(ii) 9, 13, 21, 29 , 41, 43
Shells....
5-5 Read only 
5-6(i) and(ii)
6.4 p394-395 (i) 3,5, 8 
(ii) 11,13
Work.... 
Hooke's law
2.4?
5-9 read(i) (i) Sens. Calc. I.C.1 on Probability Models 

(ii) Calculus and Probability Outline (on-line)

5-8 5.1 3,11,13,14

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OFFICE: Library 48                                        PHONE:826-4950
Hours (Tent.): MTRF 12:15-1:20 AND BY APPOINTMENT or chance!
On-line Math chat : I will frequently attend my math chatroom Tuesday and Thursday evenings at about 9:00 pm.
E-MAIL: flashman@humboldt.edu               WWW:  http://www.humboldt.edu/~mef2/
***PREREQUISITE: Math 115 or Math code 50 or permission. See also Teresa (Tami) Matsumoto's CALCULUS PREPARATION Information Page .



 
CHECKLIST FOR REVIEWING FOR THE FINAL   * indicates a "core" topic.
I. Differential Calculus: 
A. *Definition of the Derivative 
Limits / Notation 
Use to find the derivative 
Interpretation ( slope/ velocity ) 
B. The Calculus of Derivatives 
* Sums, constants, x n, polynomials 
*Product, Quotient, and Chain rules  
*Trignometric functions 
Implicit differentiation 
Higher order derivatives 
C. Applications of derivatives 
*Tangent lines 
*Velocity, acceleration, rates (related rates)  
*Max/min problems 
*Graphing: * increasing/ decreasing  
concavity / inflection 
*Extrema (local/ global)  
Asymptotes 
The differential and linear approximation  
Newton's method
D. Theory 
*Continuity (definition and implications) 
*Extreme Value Theorem /* Intermediate Value Theorem 
*Mean Value Theorem 
II. Differential Equations and Integral Calculus: 
A. Indefinite Integrals (Antiderivatives) 
*Definitions and basic theorem 
*Simple properties [ sums, constants, polynomials] 
*Substitution 
B. Euler's Method, etc. 
Euler's Method 
*Simple differential equations with applications 
Tangent (direction) fields/ Integral Curves 
C. The Definite Integral 
Euler Sums / Definition/ Estimates (endpoints/midpoints) /Simple Properties / Substitution 
*Interpretations (area / change in position) 
*THE FUNDAMENTAL THEOREM OF CALCULUS - evaluation form 
THE FUNDAMENTAL THEOREM OF CALCULUS - derivative form 
D. Applications 
*Recognizing sums as the definite integral  
*Areas (between curves).  
Volumes (cross sections- discs). Average value. Work.
 
Bonus Essay question for final:
Suppose P(t) is a positive continuous function on [a,b] that gives the velocity at time t of an object moving on a straight line. Explain using the mean value theorem why there is some number c between a and b where P(c) = 1/(b-a) òx=a x=b  P(x) dx.
Interpret this equation with either
(i) a discussion of the  velocity and position of the object with the position function given by a definite integral from time x=a to time x=t or
(ii) a discussion of the area under the graph of Y=P(x) above the X-axis from X=a to X=b and the area of a rectangle with height P(c) and width (b-a).

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